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Polyhedral Lyapunov functions for structural stability of biochemical systems in concentration and reaction coordinates

Blanchini, Franco and Giordano, Giulia LU (2015) 54th IEEE Conference on Decision and Control, CDC 2015 In Proceedings of the IEEE Conference on Decision and Control p.3110-3115
Abstract

Structural properties, independent of specific parameter values, can explain the robustness of biochemical systems. In this paper we consider the framework previously proposed by the authors to assess structural stability of biochemical reaction networks with monotone reaction rates, which considers systems in concentration coordinates, and we show that the results can be applied to systems in reaction coordinates (whose stability was first investigated by Al-Radhawi and Angeli): the same numerical test can be employed to find a polyhedral Lyapunov function and thus certify stability. Under suitable assumptions on the rank of structural matrices, we prove the equivalence between the test performed for the system in concentration... (More)

Structural properties, independent of specific parameter values, can explain the robustness of biochemical systems. In this paper we consider the framework previously proposed by the authors to assess structural stability of biochemical reaction networks with monotone reaction rates, which considers systems in concentration coordinates, and we show that the results can be applied to systems in reaction coordinates (whose stability was first investigated by Al-Radhawi and Angeli): the same numerical test can be employed to find a polyhedral Lyapunov function and thus certify stability. Under suitable assumptions on the rank of structural matrices, we prove the equivalence between the test performed for the system in concentration coordinates and in reaction coordinates. We finally illustrate the approach by examples.

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Please use this url to cite or link to this publication:
author
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
in
Proceedings of the IEEE Conference on Decision and Control
pages
6 pages
publisher
Institute of Electrical and Electronics Engineers Inc.
conference name
54th IEEE Conference on Decision and Control, CDC 2015
external identifiers
  • Scopus:84962019278
ISBN
9781479978861
DOI
10.1109/CDC.2015.7402687
language
English
LU publication?
no
id
c3ba1c7e-94fb-4043-8a24-85d8d311c323
date added to LUP
2016-07-06 15:08:00
date last changed
2016-11-28 11:55:50
@misc{c3ba1c7e-94fb-4043-8a24-85d8d311c323,
  abstract     = {<p>Structural properties, independent of specific parameter values, can explain the robustness of biochemical systems. In this paper we consider the framework previously proposed by the authors to assess structural stability of biochemical reaction networks with monotone reaction rates, which considers systems in concentration coordinates, and we show that the results can be applied to systems in reaction coordinates (whose stability was first investigated by Al-Radhawi and Angeli): the same numerical test can be employed to find a polyhedral Lyapunov function and thus certify stability. Under suitable assumptions on the rank of structural matrices, we prove the equivalence between the test performed for the system in concentration coordinates and in reaction coordinates. We finally illustrate the approach by examples.</p>},
  author       = {Blanchini, Franco and Giordano, Giulia},
  isbn         = {9781479978861},
  language     = {eng},
  pages        = {3110--3115},
  publisher    = {ARRAY(0x8ac2e88)},
  series       = {Proceedings of the IEEE Conference on Decision and Control},
  title        = {Polyhedral Lyapunov functions for structural stability of biochemical systems in concentration and reaction coordinates},
  url          = {http://dx.doi.org/10.1109/CDC.2015.7402687},
  year         = {2015},
}